Genuine Sequential Estimation Procedures for Gamma Populations using Exact Evaluation Criteria

Abstract

In this dissertation, we develop genuine two-stage sequential procedures for bounded-risk and fixed-width confidence interval estimation for Gamma distributed populations, based on exact evaluation criteria. The term "genuine" refers to the fact that, in contrast to previous methods, the procedures proposed herein are based on the combined samples from both the first and second stages, rather than ignoring the data from the first-stage sample. Accordingly, the terminal sample size and the estimate are no longer independent, which complicates the theory development significantly. The term "exact" refers to the fact the procedures are not evaluated on asymptotic or large sample theory, as is common in the literature predating this dissertation, and the derivations are based only on the properties of the underlying distribution, i.e., Gamma. The practical application of each procedure was also considered and examples are given for both problems, i.e., bounded-risk and fixed-width.